What's 10cm in depth

A tank initially contains a solution of 10 pounds of salt in 60 gallons of water. Water with 1/2 pound of salt per gallon is add

RUDIKE [14]

Salt flows into the tank at a rate of

(1/2 lb/gal) * (6 gal/min) = 3 lb/min

and flows out at a rate of

(Q(t)/60 lb/gal) * (6 gal/min) = 6Q(t) lb/min

The net rate of change of the amount of salt in the tank at time $t$ is then governed by

$\dfrac{\mathrm dQ}{\mathrm dt}=3-6Q$

Solve for $Q$ :

$\dfrac{\mathrm dQ}{\mathrm dt}+6Q=3$

$e^{6t}\dfrac{\mathrm dQ}{\mathrm dt}+6e^{6t}Q=3e^{6t}$

$\dfrac{\mathrm d}{\mathrm dt}[e^{6t}Q]=3e^{6t}$

$e^{6t}Q=\dfrac{e^{6t}}2+C$

$\implies Q=\dfrac12+Ce^{-6t}$

The tank starts with 10 lb of salt, so that Q(0) = 10. This gives us

$10=\dfrac12+C\implies C=\dfrac{19}2$

so that the amount of salt in the tank at time $t$ is given by

$\boxed{Q(t)=\dfrac{1+19e^{-6t}}2}$

4 0

3 years ago

PLEASE HELP NEED ANSWER ASAP 15 POINTS WILL MARK BRAINLIEST!!

ExtremeBDS [4]

Answer: slope = -3 and (-2,6) is a point on the line

please mark me as brainliest !!!

Step-by-step explanation:

6 0

3 years ago

How would I find the equation of the line of best fit for this table x 7 9 11 y 12.4 13 16

Dominik [7]

Answer:

Use your calculator to find the line of best fit for the data. ... Age Range, \begin {align*}x\end{align*}, 1-3, 4-6, 7-10, 11-14, 15- ... Here is a sample table for the scatterplot

4 0

3 years ago

Help me!! A water tank is 1/8 full. The tank is 3/4 full when 42 gallons of water is added to the tank. How much can the water t

chubhunter [2.5K]

Answer(s):

1.) 56 gallons

2.) 7 gallons

3.) 28 gallons

Step-by-step explanation:

Q1: How much water can the tank hold?

Based on the question, we know that 3/4 of the tank equals 42 gallons. Divide 42 by the numerator, 3.

42/3 = 14

Now, multiply 14 by the denominator, 4.

14 x 4 = 56.

So, the tank can hold 56 gallons. [If you'd like to double check this answer, take the fraction 42/56 and simplify it to get 3/4.

Q2: How much water was originally in the tank?

We know that the tank's maximum capacity is 56 gallons. So, if it was 1/8 originally full, multiply 56 by 1/8. [Remember that 56 as a fraction can be written as 56/1]

1/8(56/1) = 7

This means that the tank was originally 7 gallons full. [If you'd like to double check this answer, take the fraction 1/8 and multiply the numerator and denominator by 7. This gets you 7/56, or 7 gallons out of the total capacity, 56 gallons.]

Q3: How much water is in the tank when it is 1/2 full?

Earlier, we found out that the maximum capacity of the tank is 56 gallons. To find out how many gallons it holds when its half full, divide 56 by 2.

56/2 = 28

So, when the tank is 1/2 full, it contains 28 gallons. [If you want to double check this answer, take the fraction 28/56 and simplify it. When you do, you get 1/2.]

5 0

3 years ago

Read 2 more answers

Solve the following system of equations:

Vladimir79 [104]

Answer:

(-1,1)

Step-by-step explanation:

We can solve this by either graphing and finding ther point the lines intersect, or mathematically, I'll do both.

Graphing:

Mathematically:

−2x + 4y = 6

y = 2x + 3

See the attached graph. The lines intersect at (-1,1)

--------------------

I'll rearrange the first equation (to make it easier for me):

−2x + 4y = 6

4y = 2x + 6

y = (1/2)x + 1.5

Now lets substitute the second equation into the first so that we can eliminate y:

y = 2x + 3

[(1/2)x + 1.5] = 2x + 3

- (3/2)x = (3/2)

x = -1

If x = -1:

y = 2(-1) + 3

y = 1

The solution is x = -1 and y = 1, or (-1,1)

=================

Both approaches give us (-1,1), the solution to the system of equations. It is the only point that satisfies both equations.

3 0

1 year ago